Gauge theory of time-dependent stresses and defects: quantum defect dynamics

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Abstract
The author constructs the two-dimensional quantum field theory which governs an idealised ensemble of dislocations and disclinations, including their higher gradient elastic interactions. The action contains four gauge fields of phonons Ai, Cij and H, Dj, coupled minimally to two complex Higgs fields phi i, phi , which are the disorder fields of dislocations and disclinations, respectively. Because of the close analogy with the quantum field theory of electrons and photons, called quantum electrodynamics (QED), the new theory of defects and phonons may be named quantum defect dynamics (QDD).